The AOB angle is 20% of the AOD angle. The BOC angle is 40% of the BOD angle.

The AOB angle is 20% of the AOD angle. The BOC angle is 40% of the BOD angle. COD angle = 72 degrees. Find the AOD angle measure.

Because the BOC angle is 40% of the BOD angle, and the entire BOD angle is 100%, then the COD angle is 100% – 40% = 60% of the same angle. Let us find what the BOD angle is equal to if it is known that the COD angle is 72 °:

72/60 * 100 = 120 (°).

Because according to the condition of the problem, the angle AOB is 20% of the AOD, and the entire value of the angle AOD is 100%, then in percentage the angle BOD is 100% – 20% = 80%. Find the value of the angle AOD:

120/80 * 100 = 150 (°).

Answer: The AOD angle has a degree measure equal to 150 °.